The Google sign-in cookie only lets you sign in with one account at a time.

In the past, Google Apps accounts were cookied separately from Google Accounts, so you could sign in to both your Google Account and your Google Apps account in the same web browser.

Your Google Apps account has undergone a transition, and now functions more like a full Google Account. Your account uses the standard Google sign-in cookie, allowing you to sign in to only one account at a time.